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\title{\vspace{-2cm} \textbf{第十次课堂作业}}

\author{邵柯欣 \\学号：3200103310 \\课程名称：数据科学的数学基础}

\date{\today}

\begin{document}
\maketitle
\section{6.3}
$$f_1 = (x - 5)^2 + (y + 2)^2 - 2xy$$
$$f_2 = (1 - (y - 4))^2 + 20((x + 6) - (y - 4)^2)^2$$
$$(x_0, y_0) = (0,2), T_1 = 10, T_2 = 100$$
\subsection{1}
Solution:\\
$\bigtriangledown f1 = [2*(x-5)-2*y,2*(y+2)-2*x];$\\
$\bigtriangledown f2 = [40*((x+6)-(y-4)^2),2*(5-y) - 40*((x+6)-(y-4)^2)*2*(y-4)];$\\
$for T = 1:k1, (x,y)_T = (x,y)_{T-1} - \gamma * \bigtriangledown f$
$$\gamma_1 = 0.05, \gamma_2 = 0.0015$$\\
\begin{align}
 &T   &(x,y) \notag\\
 &1   &(0.7000,    1.6000)\notag\\
 &2   &(1.2900,    1.3100)\notag\\
 &3   &(1.7920,    1.1080)\notag\\
 &4   &(2.2236,    0.9764)\notag\\
 &5   &(2.5989,    0.9011)\notag\\
 &6   &(2.9291,    0.8709)\notag\\
 &7   &(3.2233,    0.8767)\notag\\
 &8   &(3.4886,    0.9114)\notag\\
 &9   &(3.7309,    0.9691)\notag\\
 &10   &(3.9547,    1.0453)\notag
\end{align}
\begin{align}
 &T   &x \notag\\
 &1  &(-0.1200,    1.5110)\notag\\
 &2  &(-0.1011,    1.5947)\notag\\
 &3  &(-0.1079,    1.5518)\notag\\
 &...  &(...,        ...)\notag\\
 &95   &(0.0813,    1.5271)\notag\\
 &96   &(0.0834,    1.5267)\notag\\
 &97   &(0.0854,    1.5263)\notag\\
 &98   &(0.0874,    1.5259)\notag\\
 &99   &(0.0894,    1.5255)\notag\\
 &100   &(0.0914,    1.5251)\notag
\end{align}

\subsection{2}
Proof:\\

\section{6.4}
Proof:\\
未能打开$G.scv$，无法进行具体的计算。
\section{6.5}
Proof:\\

\end{document}
